I remember ordering my first pair of platform shoes about twenty years ago. The shoes were very basic and actually did not look like shoes at all. There were two straps attached to piece of light plastic. I trained with my brother and we both increased our vertical jumps almost instantly. At the time there were only two brands available in the States. One was an actual shoe (Strength Shoes) and the other was an attachment to your sneaker (JumpSoles). The models have evolved since then but the principle is the same. Your heel is constantly in the air and there is constant tension in your calves as you stay on the balls of your feet. Most people mistakenly think that it is added weight that is attached to the shoes. Another misconception is that the platform shoe effect would be the same as standing on your toes. But the added benefit of the platform shoes is that you are actually standing in a regular stance with your ankles dorsiflexed.
The platform shoes have traditionally been marketed to basketball players that want to jump high enough to dunk a basketball. One company tried to market the platform shoes to the bodybuilding community as well. The problem was of course that a lot of bodybuilders want to have the calves of a ballet dancer, but do not want to train like one. To this day, I believe most consumers are basketball players. Coaches in general tend to be reluctant to try them.
I use the platform shoes occasionally. The do put a lot of stress on the knees and ankles, and I try therefore to use them sparingly. One of the best features is that you actually keep the calves activated through the whole workout. You can not stand in the platform shoes without tensing your calves a bit. The contrast between the high impact plyometric training and the static hold results in an amazing pump in the calf muscles.
In the early training programmes the manufacturers recommended running in the platform shoes. This has since been removed from most training programmes. It is indeed very unnatural to run in platform shoes. A better alternative for running is spike shoes with extra pieces around the spikes. This type of spike shoes have the same effect as platform shoes, but allow you to move much faster.
In the below video you can see various exercises that I tend to do in the platform shoes.
Learn more about various equipment that you can use in your outdoor training by downloading the Outdoor Edition Training Guide.